Adequate Decision Rules for Portfolio Choice Problems by T. Goodall

By T. Goodall

The writer offers the idea of portfolio selection from a brand new standpoint, recommending choice ideas that experience merits over these at present utilized in conception and perform. Portfolio selection conception depends upon anticipated values. Goodall argues that this dependence has a ancient foundation and argues that present determination principles are insufficient for many portfolio selection events. Drawing on econometric suggestions proposed for the matter of forecasting results of an opportunity scan, the writer defines adequacy standards, and proposes sufficient determination ideas for numerous situations.

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Decision rules may be characterised accordingly. 2 Rather than utilising all information provided by the entire distribution of a gamble, classical decision rules utilise only some distribution parameters, like the mean, the median or the variance. The parameters alone determine which alternative to 15 A D E Q U AT E D E C I S I O N R U L E S F O R PORTFOLIO CHOICE PROBLEMS choose. Although classical decision rules were at times considered mere approximations to decision rules which make use of the entire distribution,3 they may be treated as decision rules in their own right.

It should indeed be called a decision principle, rather than a decision rule. Until the function ϕ(u) is specified, the EU principle may recommend or describe vastly different decision behaviour. The EU principle’s widespread acceptance is due to the axiomatic embedding it has received, which goes beyond the axioms of linearity, reflexivity and transitivity. These axioms provide for the existence of a general function that indicates preferences among unspecified elements 24 of a general set. The axioms designed for the normative justification of the EU principle provide both for the existence of the risk attitude function ϕ(u) and for the mathematical form of the decision principle itself.

This does remedy the lack of subjectivity mentioned above. He proposes utilities that are proportional to the gains and inversely proportional to the wealth of the gambling individual, thus arriving at a logarithmic utility function of money 21 chapter three A N A LY S I S O F P R O M I N E N T DECISION RULES A D E Q U AT E D E C I S I O N R U L E S F O R PORTFOLIO CHOICE PROBLEMS wealth. Bernoulli’s rule thus replaces a one-to-one utility function u(r) = r by a logarithmic utility function, which in the general case can be written as u(r) = b⋅ln(r), where ln is the natural logarithm, and where b serves as a coefficient characterising the individual.

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